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Nonparametric VAE for Hierarchical Representation Learning

The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich repre- sentational power of neural networks with Bayesian meth- ods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribu- tion, thereby restricting its applications to relatively sim- ple phenomena. In this work, we propose hierarchical non- parametric variational autoencoders, which combines tree- structured Bayesian nonparametric priors with VAEs, to en- able infinite flexibility of the latent representation space. Both the neural parameters and Bayesian priors are learned jointly using tailored variational inference. The resulting model induces a hierarchical structure of latent semantic concepts underlying the data corpus, and infers accurate representations of data instances. We apply our model in video representation learning. Our method is able to dis- cover highly interpretable activity hierarchies, and obtain improved clustering accuracy and generalization capacity based on the learned rich representations.

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BIRCH详解_Bilabial

聚类特征(Clustering Feature,简称CF)是一种用来表征聚类特征的数据格式,他由以下三部分组成:簇中所含样本点的个数(用 N N N来表示)、簇中所有点的各项属性的线性和(用 L S LS LS来表示)以及簇中所有点的各项属性的平方和(用 S S SS SS来表示),假设存在簇 C = { ( 1 , 2 ) , ( 2 , 1 ) , ( 1 , 1 ) , ( 2 , 2 ) } C=\{\left(1,2\right),\left(2,1\right),\left(1,1\right),\left(2,2\right)\} C={ (1,2),(2,1),(1,1),(2,2)},那么 N = 4 N=4 N=4, L S = ( { 1 + 2 + 1 + 2 } , { 2 + 1 + 1 + 2 } ) = ( 6 , 6 ) LS=\left(\{1+2+1+2\},\{2+1+1+2\}\right)=\left(6,6\right) LS=({ 1+2+1+2},{ 2+1+1+2})=(6,6), S S = 1 2 + 2 2 + 1 2 + 2 2 + 2 2 + 1 2 + 1 2 + 2 2 = 20 SS=1^2+2^2+1^2+2^2+2^2+1^2+1^2+2^2=20 SS=12+22+12+22+22+12+12+22=20。因此这种结构具有很好的线性性质,即当需要合并两个簇时,总的聚类特性可以简单的通过两者聚类特性之和来表示。有了上述信息之后,就可以计算簇的质心以及方差(或标准差),其中方差可以用来表征簇的半径,还可以间接的计算两个簇质心之间的距离。   聚类特征树(Clustering Feature Tree,简称CF-Tree)是一棵高度平衡的树,这棵树由根节点、内部节点(或者称为非叶节点)以及叶节点,其中每个非叶节点和根节点都由形如 [ C F i , c h i l d i ] [CF_{i},child_{i}] [CFi​,childi​]的项组成, c h i l d i child_i childi​代表第 i i i个节点的子节点,而叶节点(或者称为簇)通过 C F i CF_i CFi​组成的序列来表示每个簇的特征,下图(图1)所示是一个CF-Tree实例。

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MSDN: MFC ATL COM ActiveX

Microsoft Foundation Classes (MFC) The C++ class library that Microsoft provides with its C++ compiler to assist programmers in creating Windows-based applications. MFC hides the fundamental Windows API in class hierarchies so that programmers can write a Windows-based application without needing to know the details of the native Windows API. Active Template Library (ATL) A C++ template library used to create ActiveX servers and other Component Object Model (COM) objects. ActiveX controls created with ATL are generally smaller and faster than those created with the Microsoft Foundation Classes. Component Object Model (COM) An open architecture for cross-platform development of client/server applications. It is based on object-oriented technology as agreed upon by Digital Equipment Corporation and Microsoft Corporation. COM defines the interface, similar to an abstract base class, IUnknown, from which all COM-compatible classes are derived.

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